Microstructured and photonic bandgap fibers for applications in the resonant bio- and chemical sensors

Title

:

resonant bio- and chemical sensors

Auteurs:

Authors

: Maksim Skorobogatiy

Date: 2009

Type:

Référence:

Citation

:

Skorobogatiy, M. (2009). Microstructured and photonic bandgap fibers for applications in the resonant bio- and chemical sensors. Journal of Sensors, 2009, p. 1-20. doi:10.1155/2009/524237

Document en libre accès dans PolyPublie

URL de PolyPublie:

PolyPublie URL: https://publications.polymtl.ca/3657/

Version: Version officielle de l'éditeur / Published version_{Révisé par les pairs / Refereed}

Conditions d’utilisation:

Terms of Use: CC BY

Document publié chez l’éditeur officiel

Titre de la revue:

Journal Title: Journal of Sensors (vol. 2009)

Maison d’édition:

Publisher: Hindawi

URL officiel:

Official URL: https://doi.org/10.1155/2009/524237

Mention légale:

Legal notice:

Ce fichier a été téléchargé à partir de PolyPublie, le dépôt institutionnel de Polytechnique Montréal

This file has been downloaded from PolyPublie, the institutional repository of Polytechnique Montréal

Volume 2009, Article ID 524237,20pages doi:10.1155/2009/524237

Review Article

Microstructured and Photonic Bandgap Fibers for Applications

in the Resonant Bio- and Chemical Sensors

Maksim Skorobogatiy

D´epartement de G´enie Physique, Ecole Polytechnique de Montreal, C. P. 6079, succ. Centre-ville, Montr´eal, QC, Canada H3C 3A7

Correspondence should be addressed to Maksim Skorobogatiy,maksim.skorobogatiy@polymtl.ca Received 3 March 2009; Accepted 2 June 2009

Recommended by Christos Riziotis

We review application of microstructured and photonic bandgap fibers for designing resonant optical sensors of changes in the value of analyte refractive index. This research subject has recently invoked much attention due to development of novel fiber types, as well as due to development of techniques for the activation of fiber microstructure with functional materials. Particularly, we consider two sensors types. The first sensor type employs hollow core photonic bandgap fibers where core guided mode is confined in the analyte filled core through resonant effect in the surrounding periodic reflector. The second sensor type employs metalized microstructured or photonic bandgap waveguides and fibers, where core guided mode is phase matched with a plasmon propagating at the fiber/analyte interface. In resonant sensors one typically employs fibers with strongly nonuniform spectral transmission characteristics that are sensitive to changes in the real part of the analyte refractive index. Moreover, if narrow absorption lines are present in the analyte transmission spectrum, due to Kramers-Kronig relation this will also result in strong variation in the real part of the refractive index in the vicinity of an absorption line. Therefore, resonant sensors allow detection of minute changes both in the real part of the analyte refractive index (10−6–10−4RIU), as well as in the imaginary part of the analyte refractive index in the vicinity of absorption lines. In the following we detail various resonant sensor implementations, modes of operation, as well as analysis of sensitivities for some of the common transduction mechanisms for bio- and chemical sensing applications. Sensor designs considered in this review span spectral operation regions from the visible to terahertz.

Copyright © 2009 Maksim Skorobogatiy. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. Introduction

R&D into fiber-optic bio- and chemosensors (FOSs) has made a lot of progress during the last ten years. This is due to the appealing properties of FOS such as immunity to electromagnetic interference, safety in explosive environ-ments, and potential to provide continuous quantitative and qualitative real-time analysis. Chemically sensitive thin films deposited on selected areas of optical fibers can influence the propagation of light in such fibers depending on the presence or absence of chemical molecules in the surround-ing environment [1]. A wide range of optical sensors has been developed for selective biomolecule detection. Most of them have reliability issues as they employ very fragile antibodies as sensing elements. These sensors include high refractive index waveguides [2], surface plasmon resonance sensors [3], resonant mirrors [4], and classical fiber-optical

sensors [5,6]. Most optical sensors are based on evanescent wave sensing, where the perturbations in the refractive index close to the sensor surface are probed by the exponentially decaying optical wave. Such sensors have proven to be highly sensitive in detection of small targets such as proteins and viruses, but they experience difficulties in detecting larger targets such as bacteria (0.5–5μm) since in that case much larger penetration of the evanescent field into analyte is required [7].

Microstructured Optical Fibers (MOFs), and Photonic Bandgap (PBG) fibers which are a subset of MOFs, promise a viable technology for the mass production of highly integrated and intelligent sensors in a single manufacturing step. In standard total internal reflection (TIR) fiber-based evanescent-wave sensors the fiber polymer jacket is stripped and the fiber cladding is polished to the core in order to obtain an overlap between the optical field and analyte,

with sensor sensitivity proportional to such an overlap. Compared to the conventional solid core optical fibers, MOFs offer a number of unique advantages in sensing applications. A defining feature of a microstructured fiber is the presence of air holes running along its entire length. Fiber optical properties are then determined by the size, shape, and relative position of the holes. Particularly, a unique ability of MOFs is to accommodate biological and chemical samples in gaseous or liquid forms inside of the air holes in the immediate vicinity of the fiber core [8–10]. In this context a MOF is used simultaneously as a light guide and as a fluidic channel. The MOF’s unique architecture makes it a very promising sensing platform for chemical and biological detection. First, MOFs naturally integrate optical detection with the mirofluidics, allowing for continuous on-line monitoring of dangerous samples in real-time without exposing the personnel to danger. In addition, the samples can be transferred in the enclosed MOF optofluidic system for further confirmation analysis, for example, polymerase chain reactions (PCRs) if needed. Such channels can be further functionalized with biorecognition layers that can bind and progressively accumulate target biomolecules, thus enhancing sensor sensitivity and specificity. Second, the MOF hole size is in sub-100μm rage, leading to very small fluid samples required for sensing. Third, MOF-based sensors can be coiled into long sensing cells (∼10 m), thus dramatically increasing their sensitivity. The same is impossible to achieve with traditional TIR fiber sensors as side polishing step limits sensor length to several cm. Forth, the desired MOFs can be mass-produced using commercial fiber draw tower in a very cost-effective manner. Fifth, the MOFs can potentially be scaled up into a two-dimensional array with small dimensions, which is suitable for making into portable point-of-care devices for simultaneous on-site detection of different kinds of analytes. Sixth, Photonic Bandgap fibers can be designed to guide light directly in their analyte-field hollow cores [11]. In such fibers light-analyte coupling is considerably stronger than that in evanescent sensors.

In this paper we review several MOF and PBG fiber-based resonant optical sensors, which have recently invoked strong interest due to development of novel fiber types, as well as due to development of techniques for activation of the fiber microstructure with functional materials. In resonant sensors one typically employs fibers with strongly nonuniform spectral transmission characteristics that are sensitive to changes in the real part of the analyte refractive index. Moreover, if narrow absorption lines are present in the analyte transmission spectrum, due to Kramers-Kronig relation this will also result in strong variation in the real part of the refractive index in the vicinity of an absorption line. Therefore, resonant sensors allow detection of minute changes both in the real part of the analyte refractive index, as well as in the imaginary part of the analyte refractive index in the vicinity of absorption lines. Although the operational principle of almost all fiber-based resonant sensors relies on strong sensitivity of the fiber transmission losses to the value of the analyte refractive index, particular transduction mechanism for biodetection

can vary. Consider, for example, the case of a hollow core PBG fiber featuring an analyte filled core. In one sensor implementation one can label the target biomolecules with highly absorbing particles of known absorption spectra, such as metal nanoparticles or quantum dots. The presence of such particles in the aqueous fiber core can then be quan-tified by detecting appearance of the absorption lines in the fiber transmission spectrum, or through resonant changes in the fiber transmission losses induced by variations in the real part of the core refractive index. In another implementation, a functional layer that binds specific biomolecules can be deposited on the inside of the hollow fiber core. Biomolecule binding events to such a layer can then be detected through resonant changes in the fiber transmission losses induced by variations in the real part of the layer refractive index.

In what follows we discuss two types of resonant sensors. One such sensor type relies on changes in the radiation losses of a leaky core mode due to changes in the real part of an analyte refractive index. Such a leaky mode is typically confined inside an analyte filled fiber core by a resonant reflector cladding. The term “leaky mode” generally refers to the guidance mechanism where the effective refractive index of a propagating mode is smaller than that of the fiber cladding. Such unusual modes are called leaky modes as, outside of a waveguide core, they do not exhibit a traditional evanescent decay into the cladding, but rather they radiate slowly (leak) into the cladding. Unlike in the case of common TIR fibers, leaky modes in PBG fibers are confined by the bandgap of a microstructured reflector. For a particular value of an analyte refractive index geometry of such a fiber is chosen to provide strong optical confinement of the leaky core mode. An example of a resonant sensor described above is a photonic bandgap fiber featuring a hollow core filled with analyte. When changing the real part of an analyte refractive index, resonant condition for mode confinement will change, resulting in strong changes in the modal radiation loss (seeFigure 1(a)). Detection of changes in the transmitted intensities can be then reinterpreted in terms of the changes in the real part of an analyte refractive index. Interestingly, the same sensor can also be used in a standard nonresonant interrogation mode for the detection of changes in the imaginary part of the analyte refractive index (analyte absorption), seeFigure 1(b). Even when operated in a nonresonant regime, sensitivity of the hollow core PBG fiber-based sensors is, generally, superior to that of traditional TIR fiber-based sensors due to greatly improved modal overlap with analyte.

Second sensor type considered in this review is operated in the vicinity of a phase matching wavelength between a Gaussian-like core-guided-mode and some other (high-order) mode that shows high sensitivity of its propagation properties to changes in the real part of the analyte refractive index Figure 1(b). For example, by activating fiber surface with a thin metal layer, at a specific resonant wavelength one can induce strong optical loss of a core-guided-mode due to coupling to an absorbing plasmon mode propagating at the metal/analyte interface. As plasmon mode is largely delocalized in the analyte region, wavelength of phase

Core mode Waveguide core filled with analyte Clad Clad Mo d al lo ss na n_a − Re (Δ n) na+ Re(Δn) λ na Mo d al lo ss na na+i·Im(Δn) λ (a) Co re mode Plasmon Phase matching point

Plasmon Core mode

Core Phase matching point Clad ω β na Mo d al lo ss An al yt e na na+ Re( Δn ) λ Metal (b)

Figure 1: Operational principles and schematics of the two types of the resonant optical sensors. (a) Analyte-filled hollow photonic bandgap fiber-based sensor. Transmission loss through such a sensor is very sensitive to the values of both the real and imaginary parts of the analyte refractive index. (b) Sensor operating near the phase matching point of a core-guided-mode and a second mode featuring large overlap with the analyte region. In the case of a phase matching with a plasmon mode, propagation loss of a core-guided-mode is strongly dependent on the real part of the analyte refractive index.

matching between the two modes will be very sensitive to the value of the real part of analyte refractive index.

2. Detection Strategies for

Absorption-Based Sensors

We now remind the reader some general facts about amplitude-based and spectral-based detection methodolo-gies. Particularly, we focus on fiber-based sensors that rely on detection of changes in the transmitted light intensity in the presence of a target analyte.

In the amplitude-based detection methodology one operates at a fixed wavelengthλ and records changes in the amplitude of a signal, which are then reinterpreted in terms of changes in the analyte refractive index. To characterize sensitivity of a fiber-based sensor of lengthL, one employs an amplitude sensitivity functionSa(λ, L), which is defined

as a relative change in the intensityP(δ, λ, L) of a transmitted light for small changes in the measurand δ. Note that δ can be any parameter that influences transmission properties of a fiber sensor. This includes concentration of absorbing particles in the analyte, thickness of a biolayer that can change due to capture of specific biomolecules, as well as real or imaginary parts of the analyte refractive index. Amplitude sensitivity is then defined as

Sa(λ, L)=lim δ→0 P(δ, λ, L)−P(0, λ, L) δ·P(0, λ, L) = ∂P(δ, λ, L) /∂δ|δ=0 P(0, λ, L) . (1)

Denoting,α(δ, λ) to be the fiber propagation loss at a fixed valueδ of a measurand, light intensity at the fiber output can be written as:

P(δ, λ, L)=Pin(λ) exp(−α(δ, λ)L), (2) where Pin(λ) is the light intensity launched into a fiber. Substituting (2) into (1), amplitude sensitivity function can be then expressed as:

Sa(λ, L)= ∂α(δ, λ)

∂δ|δ=0·L−. (3) As follows from (3), sensor sensitivity is proportional to the sensor lengthL. In turn, as follows from (2), the maximal sensor length is limited by the absorption loss of a fiber. Defining Pdet(λ) to be the power detection limit at which changes in the light intensity can still be detected reliably, the maximal sensor length allowed by the power detection limit can be calculated from (2) as

L=log(Pin(λ)/Pdet(λ))

α(0, λ) . (4)

Defining ηdet(λ) = log(Pin(λ)/Pdet(λ)), maximal sensitivity allowed by the power detection limit can be written using (3) as

Sa(λ)= −ηdet(λ)∂α(δ, λ) /∂δ|δ=0

α(0, λ) . (5) In all the simulations that follow we assume thatηdet(λ)=1, which allows us to characterize an inherent sensitivity of a sensor system, while separating it from the issue of a power

budget that might bring additional sensitivity enhancement. Finally, given sensor amplitude sensitivity, to estimate sensor resolution of a measurand δ, one can use expression (1). Assuming that the minimal detectable relative change in the signal amplitude is (ΔP/P)min(which is typically on the order of 1% if no advanced electronics is used), then the minimum value of a measurand that can be detected by such a sensor is

δmin= (ΔP/P)min Sa(λ) .

(6) Another popular sensing methodology is spectral-based. It uses detection of displacements of spectral singularities in the presence of a measurand with respect to their positions for a zero level of a measurand. This sensing approach is particularly effective in the resonant sensor configurations that feature sharp transmission or absorption peaks in their spectra. Defining λp(δ) to be the position of a peak in a

sensor transmission spectrum as a function of a measurand valueδ, spectral sensitivity function can be defined as

Sλ= ∂λ(δ)

∂δ|δ=0. (7) Given sensor spectral sensitivity, to estimate sensor resolu-tion of a measurand δ, one can use expression (7). Thus, assuming that the minimal detectable spectral shift in the peak position is (Δλp)_min (which is typically on the order

of 0.1 nm in the visible spectral range if no advanced optical detection is used), then the minimum value of a measurand that can be detected by such a sensor is

δmin=  Δλp  min Sλ . (8)

3. Sensing Using Analyte-Filled Hollow Core

Photonic Bandgap Fibers

We now describe the first resonant sensor type based on hollow core photonic bandgap fibers filled with ana-lyte. In their crossection PBG fibers can contain periodic sequence of micron-sized layers of different materials [11, 12] (Figure 2(a)), periodically arranged micron-sized air voids [13–15] (Figure 2(b)), or rings of holes separated by nanosupports [16, 17] (Figure 2(c)). PBG fibers are currently available in silica glass, polymer and specialty soft glass implementations. The key functionality of such fibers is their ability to guide light directly in the hollow or liquid-filled cores with refractive index smaller than the refractive index of a surrounding cladding material. Unlike microstructured fibers, PBG fibers confine light in their hollow cores by photonic bandgap effect, rather than by total internal reflection. Practically, bandgaps are defined as frequency regions of enhanced fiber transmission, and they are the result of destructive interference of the core-guided light inside of the fiber-microstructured cladding. When launching spectrally broad light into a PBG fiber, only the spectral components guided by the fiber bandgaps will reach the fiber end, while all the spectral components not

located within the bandgaps will be irradiated out near the fiber coupling end. Moreover, even in the absence of fiber material losses, core-guided-modes always exhibit radiation loss. This is a direct consequence of guidance in a core with refractive index smaller than that of a cladding. As we will soon see, core mode radiation loss can be very sensitive to the value of the real part of the refractive index of the material filling the fiber core, which can be utilized for sensor applications. Finally, PBG fibers have a tendency to improve the beam quality of guided light, while being effectively single mode in the limit of long propagation distances. This is a consequence of the fact that radiation losses (and, generally, absorption losses too) of the core-guided-modes of a PBG fiber are strongly differentiated with only a few low-order modes having small propagation losses. Thus, when exciting several modes at the fiber input end, only the modes having the lowest losses will survive till the fiber end. For historical reference we mention that before the invention of the all-dielectric PBG fibers, guidance in the hollow core fibers has been demonstrated in the context of metal coated capillaries [18,19].

We now detail some of the advantages offered by the hollow core PBG fibers for sensing applications. One has to distinguish two modes of operation of such sensors. First, is sensing of changes in the imaginary part of the analyte refractive index (analyte absorption) by detecting the presence and strength of the narrow absorption bands in the fiber transmission spectrum. This is the simplest, nonresonant application of the hollow PBG fibers for optical sensing in which one only takes advantage of large overlap of the core-guided leaky mode with analyte. In such sensors, signal strength due to analyte absorption, as well as sensor sensitivity are directly proportional to the sensor length. Recently, several experimental implementations of such absorption-based sensors have been demonstrated [10,20– 23]. Second mode of operation of a PBG fiber-based sensor is sensing of changes in the real part of the analyte refractive index by detection of shifts in the fiber bandgap position. As it will be explained in the following, such a sensor operates in the resonant regime with sensitivity that is largely independent of the sensor length.

3.1. Nonresonant Sensing. Classic perturbation theory con-siderations [24] predicts that changes in the effective refrac-tive index of a guided modeΔneffare related to the changes in the refractive indexΔna of analyte infiltrating the fiber,

through the overlap factor f defined as

Δneff=Δna·f =Re(Δna)·f + i·Im(Δna)· f

f =  analytedA|E|2 Rez·crossectiondAE∗t ×Ht , (9)

where Et, Ht are the transverse electromagnetic fields of

a fiber mode, while E is a complete electric field of a mode. Strictly speaking, expression (9) is only valid for the truly guided square integrable modes of the Total Internal Reflection (TIR) fibers. In the case of hollow-core PBG fibers

(a) (b) (c)

Figure 2: Various types of hollow core photonic bandgap fibers. (a) Bragg fiber featuring large hollow core surrounded by a periodic sequence of high and low refractive index layers. (b) Photonic crystal fiber featuring small hollow core surrounded by a periodic array of large air holes. (c) Microstructured fiber featuring medium size hollow core surrounded by several rings of small air holes separated by nano-size bridges.

the leaky modes are, generally, nonsquare integrable [25]. In this case, however, expression (9) can still be used but only approximatively. Particularly, to avoid divergence in the denominator of (9), one performs integration only over the finite fiber crossection limited by the interface between the multilayer reflector and a cladding. For the hollow core PBG fibers, detailed simulations show that f is typically larger than 0.9. The value of an overlap increases rapidly when the fiber core size increases, reaching values higher than 0.99 for even the moderate core sizes Rcore ∼ 5–10λ. Such a high value of the overlap factor is explained by high confinement of the guided mode in the fiber core (see, e.g., energy flux distribution of the core-guided-mode in the inset ofFigure 1(a)).

Expression (9) is fundamental for the analysis of non-resonant absorption-based sensors. Consider, for example, a microstructured or a hollow core fiber filled with aqueous solution. One possible biosensor implementation utilizing such fibers can, for example, monitor presence and concen-tration of specific biomolecules labeled by highly absorbing nanoparticles. In such a sensor biomolecules in the aqueous solution are purged through the fiber microstructure. Defin-ingC to be the concentration (measurand; δ = C in (1)) of the absorbing particles mixed with analyte, and assuming that nano-particle bulk absorption per unit of concentration is αC(λ), while fiber loss in the absence of nanoparticles

is αf(λ), then total fiber loss in the presence of absorbing

nanoparticles can be written using (9) as

α(C, λ)=αf(λ) + f ·C·αC(λ). (10)

In derivation of (10) we used the fact that Im(Δna)∼C·αC,

α(C, λ)∼Im(neff). By substituting (10) into (5), we now find expression for the maximal nonresonant sensor sensitivity to changes in the nano-particle concentration:

Sa(λ)= −fαC

(λ)

αf(λ). (11)

Note that as nano-particle absorption αC(λ) is completely

independent from the fiber loss αf(λ) in the absence of

nanoparticles, sensitivity (11) of a nonresonant sensor is, thus, directly proportional to the fiber lengthL ∼ 1/αf(λ).

Consequently, to increase sensor sensitivity one has to simply work with longer fibers featuring low propagation loss.

3.2. Resonant Sensing. Note that expression (9), when applied to PBG fibers, does not account for the spectral shift of the PBG fiber bandgap (seeFigure 1(a)) due to changes in the real part of the refractive index of an analyte filling the fiber core. In fact, for the hollow-core PBG fibers in place of (9) one has to use the following modified expression:

Δneff=Re(Δna)·f + i



Im(Δna)·f + Re(Δna)· frad

. (12) Here, frad is a radiation factor that describes changes in the radiation losses of a photonic bandgap guided mode due to spectral shift of a fiber bandgap caused by changes in the real part of the refractive index of an analyte filling the fiber core. To understand the radiation loss contribution in (12) one has to recall the principles of design and operation of the hollow-core PBG fibers. Consider, as an example, the case of a hollow core plastic Bragg fiber featuring a water filled core (refractive indexnw) surrounded by a Bragg reflector

(Figure 3(a)) made of a periodic sequence of two optically different materials with refractive indices nl, nh which are

assumed to be purely real [11,26]. We now design Bragg reflector to feature the fundamental bandgap in the visible at λ0=0.5 μm. The reflector layer thicknesses dl, dhhave to be

chosen in a very specific way as to guarantee the destructive interference of guided light in the periodic fiber cladding, hence efficient modal confinement in the fiber hollow core. Particularly, by choosing the reflector layer thicknesses to satisfy the quarter wave condition:

dl,h= λ0

4n2

l,h−Re (ncore)

2, (13)

one guarantees that the fundamental bandgap of a Bragg reflector is centered in the near vicinity of a design wave-lengthλ0[25].

We now consider particular implementation of a Bragg fiber having the core of radius Rcore = 25μm surrounded by 6 reflector layers withnh = 1.6, nl = 1.4 and the layer

thicknesses given by (13), wherencore=1.34. InFigure 2(b) in thick solid curve we present propagation loss of the fundamental Gaussian-likeHE11core mode of a Bragg fiber. In fact, HE11 mode plays a key role in the operation of a majority of the hollow-core based sensors as it is the easiest mode to excite with an external Gaussian-like laser source.

Rcore ncore nh nl dh dl nclad=nh (a) 0.65 0.6 0.55 0.5 0.45 0.4 0.35 λ (μm) 10−1 100 101 T otal loss (r adiation + absor ption) (dB/m) ncore=nw(λ) ncore=nw(λ) ncore=nw(λ) + 0.005 HE11 Rcore =15 μm Rcore =25 μm

Bulk water absorption

(b) 0.6 0.5 0.4 λ (μm) −50 0 50 100 150 200 250 300 350 A mplitude sensiti vit y (RIU − 1) Rcore=15μm Rcore=25μm (c)

Figure 3: Refractive index sensors based on hollow core PBG Bragg fibers. (a) Schematic of a hollow core Bragg fiber filled with aqueous analyte of refractive indexnw(λ). (b) Radiation-dominated propagation loss of a core-guided HE11mode for two Bragg fibers with core radii

Rcore =25μm (solid curve) and Rcore =15μm (thin dashed curve). When analyte refractive index changes, so does the radiation loss of

a fiber core mode (thick dashed curve). For the reference, in thin solid line we present absorption loss of distilled water in the visible. (c) Maximal amplitude sensitivity of the analyte filled Bragg fiber-based sensor for the two values of the fiber core radius. Note that amplitude sensitivity is almost independent of the fiber core radius.

While total propagation loss is a sum of the modal radiation and absorption losses, this particular fiber is operating in the Radiation-dominated regime; for comparison, bulk absorption loss of water is presented inFigure 3(b)in thin solid line. We note that modal propagation loss reaches its minimum at the center of a photonic bandgap at∼0.46μm, while increasing rapidly towards the edges of a bandgap. When changing the real part of the refractive index of an analyte filling the fiber core, resonant condition (13) is no longer satisfied, thus leading to spectral displacement of the fiber bandgap (a thick dashed line inFigure 3(b)). Therefore, even for small changes in the analyte refractive index, due to spectral shift in the position of a reflector bandgap, fiber propagation loss can vary substantially. Moreover, due to resonant nature of bandgap guiding, bandgap shift due to changes in the real part of the analyte refractive index can have a substantially stronger effect on the propagation losses of a core-guided-mode than changes in the absorption coefficient of an analyte. Particularly, in (13) one can calculate that at the operational wavelength of 0.5 μm, f 1, while frad 2.4·10−4. Therefore, change of 1 dB/m loss in the analyte absorption coefficient (Im(Δna)  0.9·10−8),

or change of Re(Δna)  3.8·10−5 in the real part of the

analyte refractive index, result in the same 1 dB/m change in the modal propagation loss.

We now investigate amplitude and spectral sensitivities of the hollow-core PBG fiber-based sensors. InFigure 3(c) we present amplitude sensitivity (5) of a Bragg fiber-based sensor to changes in the real part of the analyte refractive indexδ = Re(Δna). Note that sensitivity varies strongly as

a function of the wavelength of operation, increasing rapidly towards the bandgap edges. Inside of a bandgap and in the vicinity of a design wavelength, amplitude sensitivity is on

the order ofSa∼100 RIU−1. Assuming that 1% of change in

the amplitude of a transmitted light can be detected reliably, this results in sensor resolution of Re (Δna)min ∼ 10−4RIU. Finally, in the vicinity of a bandgap center at 470 nm the total fiber loss is ∼0.7 dB/m, thus defining the maximal sensor length to be on the order of∼6 m.

In a similar fashion, spectral sensitivity can be defined using (7) by detecting spectral shift in the bandgap center (wavelength of the fiber lowest loss) resulting in a spectral sensitivitySλ∼5300 nm/RIU. Assuming that 0.1 nm spectral

shift in the position of a bandgap center can be detected reliably, this results in the sensor resolution of Re (Δna)min∼ 2·10−5RIU, which is comparable to the resolution achieved by the amplitude method.

Interestingly, maximal sensitivity of a resonant hollow-core PBG fiber sensor does not depend strongly on the fiber length. To demonstrate that, in Figure 3(b) we also present losses of anHE11mode of a hollow core Bragg fiber, with a core radius Rcore = 15μm and otherwise identical parameters to the Bragg fiber with Rcore = 25μm. Note that losses of a smaller core fiber are almost 10 times as high as losses of a larger core fiber. This signifies that the maximal sensor length for a smaller core fiber is almost 10 times shorter than the length of a sensor based on a larger core fiber. In Figure 3(c) we also plot the maximal sensitivity (5) of a Bragg fiber-based sensor with a core radiusRcore = 15μm and note that it is almost identical to that of a larger core fiber. This interesting, while somewhat counterintuitive result is a direct consequence of the fact that in PBG fibers operating in the Radiation-dominated regime, fiber propagation loss and radiation factor are not independent parameters. Particularly, starting from (12), and assuming that the fiber loss for a neutral analyte is αf(λ),

then PBG fiber absorption lossα(Δna,λ) in the presence of

changes in the real part of the analyte refractive index is described by:

α(Δna,λ)=αf(λ) +4π

λ Re(Δna)·frad. (14) In the case of Bragg fibers operating in the Radiation-dominated regime one generally finds that frad ∼ αf(λ).

Therefore, maximal amplitude sensitivity as defined by (5) will not depend on the fiber loss, and as a consequence, it will not depend on the sensor length. This finding promises a significant advantage of PBG fiber based resonant sensors compared to their conventional absorption-based counter-parts. Particularly, compact and highly sensitive sensors that utilize short PBG fiber pieces and that do not require fiber coiling are more convenient to use, and easier to maintain than their conventional counterparts that utilize long coiled fibers.

4. Surface Plasmon Resonance-Based

Fiber Sensors

In this section we describe another type of a resonant sensor operating in the vicinity of a phase matching point between a Gaussian-like core mode of a fiber (waveguide) and another mode that has strong overlap with analyte region (see the inset of Figure 1(b)). In what follows, the mode that has strong overlap with analyte is assumed to be a plasmonic wave propagating on the metalized fiber surface facing analyte.

Propagating at the metal/dielectric interface, surface plasmons [27] are extremely sensitive to changes in the refractive index of the dielectric. This feature constitutes the core of many Surface Plasmon Resonance (SPR) sensors. Typically, these sensors are implemented in the Kretschmann-Raether prism geometry where p-polarized light is launched through a glass prism and reflected from a thin metal (Au, Ag) film deposited on the prism facet [28]. The presence of a prism allows phase matching of an incident electromagnetic wave with a plasmonic wave at the metal/ambient dielectric interface at a specific combination of the angle of incidence and wavelength. Mathematically, phase matching condition is expressed as an equality between the plasmonvector and a projection of the wavevector of an incident wave along the interface. Since plasmon excitation condition depends resonantly on the value of the refractive index of an ambient medium within 100–300 nm from the interface, the method enables, for example, detection, with unprecedented sensitivity, of biological binding events on the metal surface [29]. The course of a biological reaction can then be followed by monitoring angular [29, 30], spectral [31] or phase [32,33] characteristics of the reflected light. However, the high cost and large size of commercially available systems makes them useful mostly in a laboratory, while many important field and other applications still remain out of the reach for this method.

Using optical waveguides and fibers instead of bulk prism configuration in plasmonic sensors offers miniaturization,

high degree of integration and remote sensing capabilities. In fiber and waveguide-based sensors, one launches the light into a waveguide core and then uses coupling of a guided mode with a plasmonic mode to probe for the changes in the ambient environment. To excite efficiently a surface plasmon, the phase matching condition between a plasmon and a waveguide mode has to be satisfied, which mathematically amounts to the equality between their modal propagation constants (effective refractive indices). Over the past decade, driven by the need for miniaturization of SPR sensors, various compact configurations enabling coupling between optical waveguide modes and surface plasmonic waves have been investigated. Among others, metalized single mode, multimode and polarization maintaining waveguides and fibers, metalized tapered fibers, metalized fiber Bragg gratings [34–49] and, recently, solid core microstructured fibers [50–52], as well as planar photonic crystal waveguides [53] have been studied. In the majority of fiber imple-mentations (with an exception of microstructured fibers), one typically strips fiber polymer jacket and polishes off fiber cladding until fiber core is exposed; then, a metal layer is deposited directly onto a fiber core. Thus func-tionalized surface of a fiber core is then exposed to an analyte.

Ideally, one would use a single mode fiber or waveguide with all the power traveling in a single Gaussian-like core mode operating near the point of resonant excitation of the plasmon [37,54–58]. Gaussian shape of a core mode is important as it is best suited for the excitation by standard Gaussian laser sources. Near the point of phase matching, most of the energy launched into a waveguide core mode should be efficiently transferred into a plasmon mode. However, in the Total Internal Refraction (TIR) single mode waveguides with low refractive index-contrast, coupling with a plasmon is realized at essentially grazing angles of modal incidence on the metal layer. As follows from the basic SPR theory, coupling at such grazing incidence angles leads to an inevitable decrease of sensitivity of the SPR method. In principle, high index-contrast single mode waveguides (see Figure 4(a)) could be employed to increase the angle of modal incidence on the interface. However, in the single mode waveguide-based sensors, phase matching between plasmon and fundamental waveguide mode is typically hard to realize. This is related to the fact that the effective refractive index of a core-guided-mode is close to the refractive index of the core material, which is typically larger than 1.45 due to practical material limitations. The effective refractive index of a plasmon is close to the refractive index of an ambient medium which is typically airna =1 (gas sensing) or water

na=1.33 (biological sensing). Thus, large discrepancy in the

effective refractive indices makes phase matching between the two modes hard to achieve, with an exception of the high frequenciesλ < 600 nm, where the plasmon dispersion relation starts deviating towards higher refractive indices. Thus, due to practical limitation on the lowest value of the waveguide core and cladding refractive indices, single mode TIR waveguide-based sensors were demonstrated almost exclusively in the visible where phase matching condition is easier to enforce.

1.33 1.5 1.5 1.8 Metal 2.5 2 1.5 β(2π/a) 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5 1.55 1.6 1.65 (615 nm) (890 nm) ω (2 πc /a ) β= 1.33 ω β= 1.5 ω β= 1.8 ω Plasmon waveguide Mode (a) 1.33 1 1.8 Metal Phase matching point 2.5 2 1.5 β(2π/a) 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5 1.55 1.6 1.65 (615 nm) (890 nm) ω (2 πc /a ) β= 1.33 ω Plasmon waveguide Mode (b)

Figure 4: Band diagrams and schematics of various SPR-based integrated sensor implementations. (a) Single mode waveguide-based sensor. Dispersion relations of a core-guided-mode (solid) and a plasmon (thick dashed). Inset-sensor schematic;|H|2of a plasmon (a) and a core

mode (b). (b) Multimode waveguide-based sensor. Dispersion relations of the core modes (solid) and a plasmon (thick dashed). Inset-coupler schematic;|H|2of a plasmon (a) and a high-order mode (b) at the phase matching point (black circle).

Problems with phase matching and loss of sensitivity due to shallow angles of incidence could be, in principle, alleviated by using multimode waveguides [45–49] presented in Figure 4(b). If launched properly, modal effective prop-agation angles in such waveguides can be much steeper, also resulting in smaller effective refractive indices. However, in multimode waveguides, a large number of higher-order modes can be phase matched with a plasmon. Thus, sensitivity and stability of such sensors depend crucially on launch conditions. Moreover, as spatial field distribution in a Gaussian-like laser source is typically not well matched with the field distributions of higher-order modes of a multimode waveguide, only a small fraction of energy can be efficiently launched into such modes, thus resulting again in decreased sensitivity.

5. Plasmon-Assisted Sensing Using Solid Core

Microstructured Fibers

To alleviate the problem of phase matching of the fiber core mode and a plasmon one approach is to introduce additional geometrical features into the fiber core that could allow tuning of the fiber core mode effective refractive index [51, 59]. As mentioned before, in the case of aqueous or gaseous analytes the core mode effective refractive index has to be lowered to match that of a plasmon. As a first example of a fiber where tuning by design can be effectively achieved we consider a solid core microstructured optical

fiber shown inFigure 5(a). Such a MOF is comprised of a solid core surrounded by a ring of six air holes of diameterd1 which are placed at the vertices of a hexagon with vertice-to-vertice distanceΛ. The ring of holes works as a low refractive index cladding enabling mode guidance in the fiber core. To lower the refractive index of a core-guided-mode a small air hole of diameter dc is introduced into the fiber core

center. In place of a single hole, an array of smaller holes can be used similarly to [60]. Finally, two large semicircular channels of sized2surround the microstructured fiber core region. During sensor operation these channels are filled with analyte, and in what follows we assume that the analyte under study is distilled water with na  1.33. On a fiber

core side the channels are covered with a thin gold film of thicknessdgold40 nm–60 nm to enable plasmon excitation at the gold/analyte interface. Coupling strength between the core mode and plasmon is strongly influenced by the size d1of the holes surrounding the fiber core, (larger hole sizes result in a weaker coupling). We assume that MOF is made of a silica glass with refractive index given by one of the standard Sellmeier-type fitsnglass  1.46 [61]. Finally, the dielectric constant of gold is approximated by the Drude model:

εgold(λc)=ε∞−  λ/λp 2 1 +i(λ/λt) , (15)

where the choiceε∞ = 9.75, λt = 13μm, λp = 0.138 μm

presents one of the many possible fits of the experimental data.

As a concrete example we consider MOF with the following parametersΛ = 2μm, dc = 0.5 Λ, d1 = 0.6 Λ, d2=0.8 Λ, dgold=40 nm.

Finite element method with PML boundaries was used to find complex propagation constants of the core-guided and plasmonic modes. A typical fiber-based plasmonic sensor operates in the vicinity of a phase matching point between the core-guided-mode and a plasmon localized at the metalized surface.Figure 5(b)we present dispersion relations of the core-guided-mode (thick solid line) and a plasmon (thick dashed line). Phase matching point is located at 640 nm where the difference between the modal refractive indexes is the smallest. Detailed simulations show that by changing the size of a central hole in the range dc = 0.35 Λ–0.55 Λ, or by changing diameters of the six

holes in the ranged1 = 0.6 Λ–0.7 Λ, one can readily tune the effective refractive index of the fundamental mode by 0.01 RIU which is equivalent to 30 nm spectral tuning of the position of a plasmonic peak. Energy flux distributions in the vicinity of a phase matching point (insets (I,II) in Figure 5(b)allow clear differentiation of the nature of the two modes as being the core mode (inset (I)) and plasmonic mode (inset (II)). Due to symmetry, only a quarter of the fiber crossection is presented in the insets. In the vicinity of a phase matching point the two modes become strongly mixed (inset (III) in Figure 5(c)), with losses of a core-guided-mode increasing dramatically due to the energy transfer into the lossy plasmon mode. Core mode losses calculated as Im(neff) are presented inFigure 5(b)in a thin solid line. For the reference, losses in [dB/m] are defined asα[dB/m] =

(40π Im(neff))/(ln(10)λ[m]).

As explained earlier, detection of changes in the propa-gation loss of a core-guided-mode at the point of its phase matching with a plasmon constitutes the core of many SPR sensor implementations. We now detail plasmon-based transduction mechanism in greater details. In Figure 6(a) we present losses of the fundamental core-guided-mode in the wavelength range of 0.5 μm–1.3 μm for the same MOF design as discussed earlier. Solid line corresponds to the case of a pure analyte withna  1.33 and it features two

plasmonic excitation peaks located at 640 nm and 1120 nm. To demonstrate potential of this fiber for sensing, we present in a dashed line losses of the core-guided-mode for the case when the analyte refractive index is changed tona 1.335.

As seen from Figure 6(a) position of the first plasmonic peak (at shorter wavelengths) shifts by as much as 10 nm, which is readily detectable. From the amount of shift in the position of a plasmonic peak one can, in principle, extract the value of changes in the analyte refractive index. This transduction mechanism is commonly used for the detection of the analyte bulk refractive index changes, as well as monitoring of formation of the nanometer-thin biolayers on top of a metalized sensor surface.

Interestingly, when analyte refractive index is varied the position of the second plasmonic peak in Figure 6(a)stays mostly unchanged. Therefore, such a peak cannot be used for sensing changes in analyte refractive index. Nevertheless, presence of such a peak is very useful as it serves as a natural reference in the measurements, which simplifies greatly data

acquisition and data interpretation. To understand better the nature of the two plasmonic peaks, in the insets ofFigure 6(a) we present energy flux distributions in the core-guided core modes evaluated at the first and second plasmonic peaks. From the pictures one notices that at the first peak (inset (I), Figure 6(a)) the plasmon contribution to the hybrid mode is delocalized in the analyte region, while at the second peak (inset (II),Figure 6(a)) the plasmon contribution to the hybrid mode is delocalized mostly in the fiber cladding. This explains why spectral position of the first peak is considerably more sensitive to the changes in the analyte refractive index than that of a second peak.

Finally, inFigure 6(b)we present amplitude sensitivity of the MOF sensor to changes in the real part of the analyte refractive index as defined in (5) (δ = Re(Δna)). Sensor

sensitivities are calculated for several values of the gold layer thickness. Maximal sensitivitySa ∼ 180 RIU−1 is achieved

for a 40 nm thick gold film. Assuming that 1% of change in the amplitude of a transmitted light can be detected reliably, this results in sensor resolution of Re (Δna)min ∼ 6·10−5RIU. Finally, at the wavelength of maximal sensor sensitivity at 665 nm the total fiber loss is∼150 dB/cm, thus defining the maximal sensor length to be on the order of

∼1 mm. In passing we note that plasmon being a surface excitation is very sensitive to the thickness of a metallic layer. This can be used to study metal nanoparticle binding events on the metallic surface of a sensor [62]. This mode of sensor operation can be of interest, for example, to the monitoring of concentration of metal nanoparticles attached to the photosensitive drugs in the photodynamic cancer therapy [63].

6. Plasmon-Assisted Sensing Using Solid Core

Photonic Bandgap Fibers

As mentioned in the previous section, introduction of additional geometrical features into the fiber core could allow tuning of the fiber core mode effective refractive index. However, in the case of TIR-microstructured fibers the tuning range, while significant (0.01 RIU as shown in the previous section), is not sufficient to alleviate the problem of phase matching of the fiber core mode and a plasmon. The problem of phase matching becomes especially pronounced in the case of low refractive index analytes. In what follows, we detail design principles of the photonic bandgap fiber and waveguide-based SPR sensors, and show that in such sensors the fundamental Gaussian-like leaky core mode can be phase matched with a plasmon at any desired wavelength of operation from the visible to mid-IR, and for any value of the analyte refractive index. Effectively, PBG waveguide-based sensors integrate advantages of both the multimode and single mode waveguide-based SPR sensors by being able to reduce the core mode refractive index to any desired value (even 0), while operating with a Gaussian-like core mode.

To remind the reader, the term “leaky mode” gener-ally refers to the guidance mechanism where the effective refractive index of a propagating mode is smaller than that of the waveguide cladding. Such unusual modes are called

Analyte Gold layers d2 d1 dc Λ na (a) (I) (I) (II) (II) (III) (III) 3 3 2 2 1 1 0 0 3 3 2 2 1 1 0 0 3 3 2 2 1 1 0 0 0.8 0.75 0.7 0.65 0.6 0.55 0.5 λ (μm) 1.42 1.43 1.44 1.45 Re (neff ) (μ m) (μ m) (μ m) (μm) (μm) (μm) 0 1 2 3 Im (neff ) × 10 − 4 (b)

Figure 5: (a)Schematics of a MOF-based SPR sensor. The fiber comprises six air holes surrounding a solid fiber core. These holes form a microstructured cladding with low effective refractive index. A smaller hole is introduced in the core center to enable tunability of the core mode effective refractive index to facilitate phase matching with a plasmon. Two large semicircular metalized channels are integrated into the fiber structure to enable efficient microfluidic flow of analyte and plasmon excitation at the metal/analyte interface. (b) Dispersion relations of a core-guided-mode (thick solid line) and a surface plasmon (thick dashed line) in the vicinity of the phase matching point. Insets (I), (II) show energy fluxes of the core-guided and plasmon modes close to the phase matching point. Transmission loss of a core-guided-mode (thin solid line) exhibits strong increase at the phase matching point due to efficient mixing with a plasmon as confirmed by its energy flux distribution (inset (III)).

Peak I Peak II 3 3 2 2 1 1 0 0 (μm) (μ ) m 3 3 2 2 1 1 0 0 (μm) (μ ) m Peak II Peak I 1.3 1.1 0.9 0.7 0.5 λ (μm) 0 50 100 150 200 250 300 Loss (d B/cm ) na=1.33 na=1.335 (a) 40 nm _{50 nm} 65 nm 0.7 0.65 0.6 λ (μm) −150 −100 −50 0 50 100 150 200 A mplitude sensiti vit y (RIU − 1) (b)

Figure 6: Calculated loss spectra of the fundamental core-guided-mode of a metalized MOF. Loss spectrum (solid curve) features several attenuation peaks corresponding to the excitation of plasmonic modes on the surface of metalized channels filled with aqueous analyte of refractive index 1.33. By changing the analyte refractive index (dotted curve), resonant attenuation peaks corresponding to the points of phase matching between the core-guided and plasmon modes shift. In the insets, energy flux of a core-guided-mode is presented at the two absorption peaks. Spectral position of the peak I is the most sensitive of the two peaks to changes in the analyte refractive index. This is because the corresponding core mode is coupled to a plasmon with a strong presence in the analyte region in contrast to the peak II at which plasmonic mode is predominantly extended into the cladding region.

leaky modes as, outside of a waveguide core, they do not exhibit a traditional evanescent decay into the cladding, but rather they radiate slowly (leak) into the cladding. Unlike in the case of common TIR waveguides, leaky modes in photonic crystal waveguides are confined by the bandgap of

a photonic crystal reflector. As a consequence, the effective refractive index of the fundamental (lowest loss) leaky core mode can be designed to be arbitrarily smaller than that of a waveguide core material, thus enabling phase matching with a plasmon at any desired frequency. Moreover, the lowest loss

leaky core mode typically exhibits a Gaussian-like intensity distribution in the waveguide core region, thus enabling convenient excitation by a Gaussian beam of an external light source. Using the fundamental (lowest loss) leaky mode for sensing gives the additional advantage of an effectively single mode propagation regime. In particular, when a set of modes is excited at a sensor input, higher-order leaky modes radiate out faster than a fundamental mode. Consequently, after a certain propagation distance, only the fundamental mode is left in the waveguide core. Finally, the effective angle of modal incidence onto a metal film, and hence sensitivity, can be varied at will by a proper selection of the waveguide core and reflector materials.

6.1. SPR Sensors Using Planar Photonic Bandgap Waveg-uides. To demonstrate the principles of operation of pho-tonic bandgap waveguide-based SPR sensors we start by considering plasmon excitation by a Gaussian-like TM-polarized mode of a planar photonic crystal waveguide (see Figure 7(a)), in which light confinement in a lower refractive index core is achieved by a surrounding multilayer reflector. TM polarization of the electromagnetic field in a planar multilayer assumes a single magnetic field component|H|2 directed parallel to the plane of a multilayer, while the electric field component is confined to a plane perpendicular to the multilayer.

The photonic crystal waveguide under consideration consists of 27 alternating layers having refractive indices nh = 2.0, and nl = 1.5. The core layer is layer number

12; having refractive indexnc =nl. Analyte (first cladding)

is waterna = 1.332 bordering a 50 nm layer of gold. The

substrate refractive index is 1.5. Theory of planar photonic crystal waveguides with infinite reflectors where nc = nl

[64], predicts that, for a design wavelengthλc, the effective

refractive indexneff(λc) of the fundamental TE and TM

core-guided-modes can be designed at will, as long as 0< neff< nl,

by choosing the reflector layer thicknesses as dl,h= λc

4n2

l,h−n2eff

, (16)

and by choosing the core layer thickness as dc = 2dl.

Moreover, for this choice ofnc, the field distribution in the

core is always Gaussian-like for TE-polarized modes, while for TM-polarized modes it is Gaussian-like as long asn2

eff> εlεh/(εl+εh) [64]. By choosing the effective refractive index

of a core mode to be that of a plasmon, a desired phase matching condition is achieved. For a waveguide with a finite reflector, the same design principle holds approximately. Thus, for an operating wavelength ofλ=640 nm, considered in this example, phase matching is achieved when the photonic crystal waveguide is designed usingλc = 635 nm

and Re(neff(λc))=1.46 in (16). A reasonable approximation

to the neff(λc) is a value of the effective refractive index

of a plasmonic wave propagating at a planar gold-analyte interface: neff(λc)=  εgold(λc)·εa(λc) εgold(λc) +εa(λc) 1/2 , (17)

whereεa is the dielectric constant of an analyte andεgold is the dielectric constant of the gold layer approximated by the Drude model (15).

In Figure 7(b) we present band diagram of a planar photonic crystal waveguide-based SPR sensor. All the simu-lations are performed using standard transfer matrix theory on a complete system that includes both the waveguide and metal layer. Gray regions signify bulk states of a periodic reflector. The clear region is a TM bandgap where no extended into the reflector states are found. The thick solid line, which is almost parallel to the band gap edges, marked as “core mode” is a dispersion relation of a Gaussian-like leaky core mode with most of its modal energy concentrated in the low refractive index core. The dashed line marked as “plasmon” represents the dispersion relation of a plasmonic mode. Most of the plasmon energy is concentrated at the metal/analyte interface.

Near the phase matching point, fields of a core-guided-mode contain strong plasmonic contribution. As plasmon exhibits very high propagation loss, the loss of a core mode (upper plot inFigure 7(c)) will also exhibit a sharp increase near the phase matching point with a plasmon. An important aspect of the proposed setup is the freedom of adjusting the loss of a core mode. As leaky mode decays exponentially fast with respect to distance into the multilayer reflector, coupling strength between the plasmon and core modes can be controlled by changing the number of reflector layers situated between the waveguide core and a metal film. Ultimately, higher coupling strength leads to higher modal losses, hence, shorter sensor length. When the real part of the analyte refractive index is varied, the plasmon dispersion relation displaces accordingly, thus leading to a shift in the position of the phase matching point with a core-guided-mode. Consequently, in the vicinity of the phase matching point, transmission loss of a core-guided-mode varies strongly with changes in the analyte refractive index (see the upper part ofFigure 7(c)).

We would like to point out that what is identified as a “core mode” in all the figures in this paper is in fact a waveguide supermode that includes both the core-guided-mode and plasmonic contribution. Since the plasmon core-guided-mode is extremely lossy, only a small mixing of this mode with the core mode is necessary to achieve sensing. We found pertinent to also show on the graphs what a plasmonic mode looks like near the phase matching point, although this mode by itself is not used in our sensing arrangements. Depending on the designs, the plasmon contribution to the evanescent tail of a core mode is not always visible on the field distribution plots as only the real components of the modes are truly phase matched.

The simplest mode of operation of a waveguide-based SPR sensor is detection of small changes in the bulk refractive index of an analyte. Similarly to the case of hollow core PBG fiber-based sensors, there are two main modalities of SPR detection-amplitude-based and spectral-based. In both methodologies sensing is enabled through detection of changes in the location of a sharp plasmonic loss peak which spectral position is strongly dependent on the value of the ambient refractive index. In the amplitude-based

Gold layer = 2 = 1.5 Substrate Core Plasmon Core mode 0 1 2 4 5 3 6 7 8 9 n_h n_l na (μ m) (a) TM bandgap Plasmon Core mode 0.7 0.68 0.66 0.64 0.62 0.6 λ (μm) 1.4 1.42 1.44 1.46 1.48 1.5 1.52 1.54 Re (neff ) na∼1.33 ncore (b) 0.7 0.68 0.66 0.64 0.62 0.6 0 1 2 3 4 5 6 7 Loss (d B/cm ) na=1.332 na=1.342 0.7 0.68 0.66 0.64 0.62 0.6 λ (μm) −120 −80 −40 0 40 80 Sensiti vit y (1/RIU) (c)

Figure 7: Planar photonic bandgap waveguide-based SPR sensor. (a) Schematic of a sensor. Low refractive index core is surrounded by the periodic photonic crystal reflector. Top side of the reflector is goldplated for plasmon excitation. Gold layer is bordered by aqueous analyte.|H|2field distribution in the fundamental core mode is shown on the right, while field distribution in a plasmonic mode is show

on the left of a sensor schematic. (b) Band diagram of sensor modes. Dispersion relation and field distribution of the fundamental core mode (thick solid curve), and plasmonic mode (dashed curve). TM bandgap of a periodic reflector is shown as a clear region, while gray regions correspond to the continuum of the bulk reflector states. By design, the effective refractive index of a core-guided-mode can be made significantly smaller than that of the waveguide core material. (c) Upper part: solid curve shows loss of a waveguide core mode near the phase matching point with a plasmon at which modal loss peaks. Dashed line shows shift of the modal loss curve when refractive index of the analyte is varied. Lower part: dependence of the sensor amplitude sensitivity on wavelength.

approach, all the amplitude measurements are performed at a single wavelength near the center of a plasmonic peak. The advantage of this method is its simplicity and low cost, as no spectral manipulation is required. The disadvantage is a smaller dynamic range and lower sensitivity when compared to the wavelength interrogation approach, in which the whole transmission spectra are taken and compared before and after the change in the analyte has occurred. We now use expression (5) to define sensor amplitude sensitivity with respect to changes in the real part of an analyte refractive index. In (5) the measurand δ is Re(Δna), and α(δ, λ) is

propagation loss of a core-guided-mode presented at the top ofFigure 7(c). At the bottom ofFigure 7(c)we present amplitude sensitivity of a PBG waveguide-based SPR sensor as a function of the wavelength of operation. Maximal sensitivity is achieved at 673 nm and is equal to 112 RIU−1. It is typically a safe assumption that 1% change in the transmitted intensity can be detected reliably, which leads to a sensor resolution of 9·10−5RIU. In the wavelength interrogation mode, changes in the analyte refractive index are detected by measuring displacement of a plasmonic peak center wavelengthλp as a function of the value of an

analyte refractive index. Sensor sensitivity is then defined by expression (7), whereδ=Re(Δna). We find that the spectral

sensitivity of a PBG waveguide-based sensor is 2300 nm·

RIU−1. Assuming that a 0.1 nm change in the position of a resonance peak can be detected reliably, sensor resolution of 4.3·10−5RIU is obtained.

Finally, sensor length is always in the rangeL∼1/α(δ, λ). In the vicinity of plasmonic peak shown in Figure 7(c)

typical sensor length isL∼1 cm. Detailed simulations also show that similarly to the case of resonant sensing using hollow core PBG fibers, sensitivity of a PBG waveguide-based plasmonic sensor is only weakly dependent on the sensor length. Particularly, by varying the number of reflector layers separating the waveguide core and gold layer one can vary the overall sensor length from sub-mm to several cm without changing significantly the sensor sensitivity.

In the rest of this section we present theoretical study of SPR sensor designs based on photonic bandgap fibers, rather than planar waveguides. Advantages of fiber based sensors over their planar counterparts include lower manufacturing cost, possibility of distributed sensing, and incorporation of microfluidics into the fiber structure directly at the fiber drawing step. In what follows we demonstrate an SPR sensor using solid core PBG Bragg fiber operating at 760 nm, as well as an SPR sensor using honeycomb lattice photonic bandgap fiber operating at 1060 nm.

6.2. SPR Sensors Using Photonic Bandgap Bragg Fibers. We start by describing solid core Bragg fiber-based SPR sensor for detection in aqueous analytes. In such a sensor a thin gold layer is deposited on the outer surface of a Bragg fiber in direct contact with an analyte. By tailoring the dispersion relation of the core-guided-mode of a Bragg fiber, phase matching with a plasmon can be obtained at any wavelength in the visible and near-IR. The mode of operation in such a sensor is a Gausian-likeHE11core mode. Effective refractive index of such a mode is matched with that of a plasmon by the proper choice of the fiber core size. The choice of anHE11

mode over the other modes is motivated by the ease of its excitation using common Gaussian laser sources.

As an example we consider solid core photonic crystal Bragg fibers made of two materials with refractive indices nl =1.42 and nl=1.6. Prototypes of such fibers have been

recently fabricated in our group by using a poly(vinylene difloride) (PVDF)/polycarbonate (PC) material combina-tion [65]. In such fibers, a solid core of refractive indexnlis

surrounded by N alternating high and low refractive index reflector layers of thicknesses dl, and dh (see Figure 8(a)).

In a manner similar to the planar multilayer waveguides, reflector layer thicknesses are given by the quarter wave condition (16), where λc is an operating wavelength, and

neff(λc) is a desired effective refractive index of a

core-guided-mode at that wavelength. Although such a choice of the reflector parameters guarantees bandgap guidance at λc of

a mode with effective refractive index neff(λc), however, it

does not guarantee existence of such a mode. One way of positioning a core mode dispersion relation inside of the reflector bandgap is by varying the fiber core diameter dc. Namely, in the large core diameter Bragg fibers with

dc  λc, effective refractive index of the fundamental core

mode is close to that of the core material. By decreasing the fiber core size, one can consistently reduce the core mode effective refractive index, and, eventually, position it in the middle of the reflector bandgap. Moreover, in the context of SPR sensing, λc also corresponds to the wavelength of

phase matching between plasmon and a core-guide mode. Therefore, a good approximation toneff(λc) of a

core-guided-mode is that of the effective refractive index of a plasmonic wave propagating at a planar gold-analyte interface given by (17). With these choices ofneff(λc) and dc we are still

left with one free parameter, which is the number of layers N in the Bragg reflector. In metalized Bragg fibers, guided modes incur additional losses due to high absorption in the metal film. When operating within bandgap of a Bragg fiber reflector, the fields of leaky core modes decay exponentially fast into the reflector. Therefore, modal presence in the metal layer also decreases exponentially fast when increasing the number of reflector layers. Thus, the choice of the number of reflector layers primarily effects the core mode propagation loss, and, consequently, sensor length. As was mentioned earlier, PBG fiber-based sensor sensitivity is only weekly dependent on sensor length. Therefore, without the loss of sensitivity, one would choose a small enough number of reflector layers, so that the resultant fiber is short enough to prevent the necessity of coiling and simplify sensor handling. InFigure 8we present an example of a solid core PBG fiber-based SPR sensor. By choosing the fiber core size to be small, one can considerably reduce the effective refractive index of the core mode. This enables plasmonic excitation at longer wavelengths in the near-IR. InFigure 8(a) we show cross-section of a small-core Bragg fiber-based sensor, as well as energy flux distributions in the HE11 core mode and plasmonic mode. Reflector layer thicknesses are chosen according to (16), where λc = 760 nm,nl = 1.42, nh =

1.6, and neff = 1.39, thus resulting in nl = 654 nm,

nl = 240 nm. Fiber core diameter is dc = 1.8 μm. The

total number of layers is N = 12. For the fundamental

Gaussian-like mode, the amount of energy in the core is 78%. In Figure 8(b) we present the band diagram of the modes of thus defined Bragg fiber sensor. Common TM, TE bandgap of a corresponding infinitely periodic Bragg reflector is presented as a clear region, while gray regions define a continuum of reflector bulk states. In a small core Bragg fiber, the effective refractive index of the core-guided HE11 mode (thick solid line) can be considerably smaller than the refractive index of a core material (thin solid line). Dispersion relation of a plasmon mode is shown as thick dashed line. In this particular case, the dispersion relation of the core-guided-mode is shifted towards the lower edge of the reflector bandgap, therefore, the core mode (solid curve inFigure 8(a)) and plasmonic mode (dashed curve in Figure 8(a)) penetrate significantly into the reflector. Phase matching between the core and plasmonic modes is achieved at 758 nm. In the upper plot of Figure 8(c), propagation loss of the core-guided-mode is presented as a function of the wavelength. As seen from this plot, core mode loss peaks at the wavelength of phase matching with plasmon mode. In the lower plot ofFigure 8(c), we present amplitude sensitivity (5) of a solid core Bragg fiber-based SPR sensor with respect to changes in the real part of the analyte refractive index. Maximal sensitivity is achieved at 788 nm and is equal to 293 RIU−1. Assuming that a 1% change in the transmitted intensity can be detected reliably, this leads to a sensor resolution of 3.4·10−5RIU. Finally, we find that the corresponding spectral sensitivity (7) is 104_nm·RIU−1_. Assuming that a 0.1 nm change in the position of a resonance peak can be detected reliably, this leads to a sensor resolution of 9.8·10−6RIU. The sensor length in this case is in a 1 cm range.

6.3. SPR Sensors Using Photonic Bandgap Honeycomb Fibers. In the two previous subsections we have presented design strategies for the SPR sensors based on a PBG Bragg waveguide and a PBG Bragg fiber. In principle, any photonic bandgap fiber can be used in place of a Bragg fiber to develop such sensors. In this section we present an example of a SPR sensor based on a solid core honeycomb PBG fiber.

In Figure 9(a) schematic of a honeycomb photonic crystal fiber-based SPR sensor is presented. The design parameters are chosen as follows, the center-to-center dis-tance between adjacent holes isΛ = 0.77 μm, the cladding hole diameter is d = 0.55 Λ, the diameter of the hole in the core center isdc = 0.35 Λ. The fiber is made of silica

glass with a refractive index ofnglass = 1.45, the core and cladding holes are filled with air nair = 1, while the large semicircular channels are plated with a 40 nm thick layer of gold and filled with an aqueous analytena = 1.32. The

central hole in the fiber core lowers its effective refractive index compared to that of a silica cladding. Under certain conditions, such a core can support a mode confined by the bandgap of the honeycomb reflector. The core-guided-mode in such a fiber is analogous to that of the small solid core Bragg fiber discussed earlier. Guided by the bandgap of the fiber reflector, the effective refractive index of the core mode can be made much lower than that of the silica material.